Date: Jan 16, 2013 3:34 AM
Author: Jussi Piitulainen
Subject: Re: simplifying rational expressions
stony writes:

> Need a little help with this. We are simplifying the following, but

> the solution is pretty lengthy and messy because of the enormous

> number of factors. I was thinking that may be I am missing seeing a

> pattern (some series or something). Is grunt work the only way to

> solve this or is there a pattern that can simplify the whole process?

>

> My daughter was trying to solve this, but ended up with the mess and

> then I got the same mess, but I thought there may be an easy way to

> simplify this that I may be missing.

>

> ((b-c)/((a-b)(a-c))) + ((c-a)/((b-c)(b-a))) + ((a-b)/((c-a)(c-b))) +

> (2/(b-a)) - (2/(c-a))

>

> of course, I took all the factors in the denominator and then started

> multiplying the numerator with the remaining factors to end up with a

> mess.

I suspect you are missing the fact that (a - b) and (b - a) in the

denominators are essentially the same factor. The common denominator

of the terms is (a - b)(a - c)(b - c). I think you can leave the

denominator in that form.

I did the numerator two ways: in terms of these same factors, and

multiplying out and combining terms. They seemed about equally simple

to me, though I may have made mistakes. I usually do. Be careful with

the signs :)

Hope this helps.